Metal looks different in lookdev and render
Cycles Render View


Cycles Lookdev View


I would say you don't use the same lightning setup for render and lookdev. Render use World and Scene Lights / Lookdev Studio light.

In the file you provided I can't confirm you use studio HDR for render, also if would use the same HDR for lookdev and  render, difference will does studio lights that are not taken into lightning in lookdev.



If I (for example) disable Studio Lights and Scene World I can see Render and Lookdev in both Cycles and Eevee matchs.